Question

1. (15 points) The mass of Earth is 5.97 x 1027 grams. In this problem, you will compare various objects to Earth’s mass.

A. The mass of a ping-pong ball is 2.3 grams. How many ping-pong balls would it take to equal the mass of Earth?

B. The mass of the moon is 7.36 • 1025 grams. To the nearest tenth, how many moons would it take to equal the mass of Earth?

C. The mass of the sun is 1.99 • 1033 grams. Use a reasonable approximation to quickly calculate how many Earths it would take to equal the mass of the sun.

Answer 1

HEYA MATE YOUR ANSWER IS

The gravitational force can be calculated with the formula: ... G= gravitational constant. M= mass of ... R= distance from earth's centre to object's centre.

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Answer 2

The answers are -

The answers are - (A) 3 × 10⁷ balls

The answers are - (A) 3 × 10⁷ balls (B) 81.1 moons

The answers are - (A) 3 × 10⁷ balls (B) 81.1 moons (C) 3 × 10⁵ Earths

GIVEN

Mass of the earth = 5.97 × 10²⁷ grams

Mass of ping-pong ball = 2.3 grams

Mass of the moon = 7.36 × 10²⁵ grams

Mass of the sun = 1.99 × 10³³ grams

TO FIND

(a) Number of ping pong balls

(b) Number of moon

(C) Number of Earths

SOLUTION

(A) Number of ping-pong balls

We can simply solve the above problem as follows,

Mass of Earth = 5.97 × 10²⁷ grams

Mass of 1 Ping pong ball = 2.3 grams

We can observe That,

2.3 grams = 1 pingpong ball

1 gram = 1/2.3 ping pong balls

Pingbong balls equal to the weight of Earth = 5.97 × 10²⁷ / 2.3

Dividing 5.97 by 2.3

= 2.5 × 10²⁷

Rounding the decimal to nearest whole number

= 3 × 10⁷ balls

(B) Number of moons required

Mass of the moon = 7.36 × 10²⁵ grams

We can also write it as,

7.36 × 10²⁵ grams = 1 moon

1 gram = 1/7.36 × 10²⁵ moon

So,

Number of moons that equals weight of the earth = 5.97 × 10²⁷ / 7.36 × 10²⁵

Dividing 5.97 by 7.36 and bringing 10²⁵ to the numerator by reversing the sign of exponent.

= 0.81 × 10²⁷ × 10⁻²⁵

= 0.811 × 10²

= 81.1

Hence, It will 81.1 moons

(C)

Mass of the Sun = 1.99 × 10³³ grams

Given,

Mass of the Earth = 5.97 × 10²⁷ grams

So,

Number of Earths weighing 5.97 × 10²⁷ grams = 1

Number of earths weighing 1 gram = 1/5.97 × 10²⁷ moons

Number of earth weighing 1.99 × 10³³ grams = 1.99 × 10³³ grams /5.97 × 10²⁷

Dividing 1.99 by 5.97 and bringing 10²⁷ on numerator by reversing the sign of the exponent;

= 0.33 × 10³³ × 10⁻²⁷

We know that, When base is same the exponents are added,

Therefore,

= 0.3 × 10⁶

Approximating the above number to nearest whole number

= 3 × 10⁵ Earths

Hence, The answers are -

Hence, The answers are - (A) 3 × 10⁷ balls

Hence, The answers are - (A) 3 × 10⁷ balls (B) 81.1 moons

Hence, The answers are - (A) 3 × 10⁷ balls (B) 81.1 moons (C) 3 × 10⁵ Earths

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